Approximately,
\[
\begin{alignedat}{4}
A^\prime_{\mathbf{6}}&{}\approx{}&0.577350269190&{}:{}&0.211324865405&{}:{}&0.211324865405&,\\B^\prime_{\mathbf{6}}&{}\approx{}&0.211324865405&{}:{}&0.577350269190&{}:{}&0.211324865405&,\\C^\prime_{\mathbf{6}}&{}\approx{}&0.981125224325&{}:{}&0.981125224325&{}:{}&-0.962250448649&,
\\
A^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.347748149397&{}:{}&0.648906880894&{}:{}&0.003344969709&,\\B^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.648906880894&{}:{}&0.347748149397&{}:{}&0.003344969709&,\\C^{\prime\prime}_{\mathbf{6}}&{}\approx{}&0.394337567297&{}:{}&0.394337567297&{}:{}&0.211324865405&,
\\
A^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.363466037631&{}:{}&0.993007681634&{}:{}&-0.356473719264&,\\B^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.993007681634&{}:{}&0.363466037631&{}:{}&-0.356473719264&,\\C^{\prime\prime\prime}_{\mathbf{6}}&{}\approx{}&0.422649730810&{}:{}&0.422649730810&{}:{}&0.154700538379&,
\\
A^*_{\mathbf{6}}&{}\approx{}&0.000000000000&{}:{}&1.077350269190&{}:{}&-0.077350269190&,\\B^*_{\mathbf{6}}&{}\approx{}&1.077350269190&{}:{}&0.000000000000&{}:{}&-0.077350269190&,\\C^*_{\mathbf{6}}&{}\approx{}&0.500000000000&{}:{}&0.500000000000&{}:{}&0.000000000000&.
\end{alignedat}
\]